The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting
In this article, we propose a novel integral transform coined as quaternion quadratic phase S-transform (Q-QPST), which is an extension of the quadratic phase S-transform and study the uncertainty principles associated with the Q-QPST. The Q-QPST possesses some desirable characteristics that are abs...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2024-0077 |
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| author | Gargouri Ameni |
| author_facet | Gargouri Ameni |
| author_sort | Gargouri Ameni |
| collection | DOAJ |
| description | In this article, we propose a novel integral transform coined as quaternion quadratic phase S-transform (Q-QPST), which is an extension of the quadratic phase S-transform and study the uncertainty principles associated with the Q-QPST. The Q-QPST possesses some desirable characteristics that are absent in conventional time-frequency transforms, especially for dealing with the time-varying quaternion-valued signals. First, we propose the definition of Q-QPST and then we explore some mathematical properties of the of quaternion Q-QPST, including the linearity, modulation, shift, orthogonality relation, and reconstruction formula. Second, we derive the associated Heisenberg’s uncertainty inequality and the corresponding logarithmic version for Q-QPST. Finally, an illustrative example and some potential applications of the Q-QPST are introduced. |
| format | Article |
| id | doaj-art-2bc6eea9d6be4b48bb98b9ac815a6969 |
| institution | DOAJ |
| issn | 2391-4661 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-2bc6eea9d6be4b48bb98b9ac815a69692025-08-20T02:56:33ZengDe GruyterDemonstratio Mathematica2391-46612024-11-0157174975910.1515/dema-2024-0077The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion settingGargouri Ameni0Mathematics Department, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Al-kharj, Riyadh 11912, Saudi ArabiaIn this article, we propose a novel integral transform coined as quaternion quadratic phase S-transform (Q-QPST), which is an extension of the quadratic phase S-transform and study the uncertainty principles associated with the Q-QPST. The Q-QPST possesses some desirable characteristics that are absent in conventional time-frequency transforms, especially for dealing with the time-varying quaternion-valued signals. First, we propose the definition of Q-QPST and then we explore some mathematical properties of the of quaternion Q-QPST, including the linearity, modulation, shift, orthogonality relation, and reconstruction formula. Second, we derive the associated Heisenberg’s uncertainty inequality and the corresponding logarithmic version for Q-QPST. Finally, an illustrative example and some potential applications of the Q-QPST are introduced.https://doi.org/10.1515/dema-2024-0077quadratic-phase transformquaternion quadratic-phase s-transformmodulationuncertainty principle42a0542b1046s1042c2044a35 |
| spellingShingle | Gargouri Ameni The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting Demonstratio Mathematica quadratic-phase transform quaternion quadratic-phase s-transform modulation uncertainty principle 42a05 42b10 46s10 42c20 44a35 |
| title | The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting |
| title_full | The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting |
| title_fullStr | The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting |
| title_full_unstemmed | The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting |
| title_short | The novel quadratic phase Fourier S-transform and associated uncertainty principles in the quaternion setting |
| title_sort | novel quadratic phase fourier s transform and associated uncertainty principles in the quaternion setting |
| topic | quadratic-phase transform quaternion quadratic-phase s-transform modulation uncertainty principle 42a05 42b10 46s10 42c20 44a35 |
| url | https://doi.org/10.1515/dema-2024-0077 |
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